Question 1

Which of the following relations is a function?

Accepted Answer

$\{(2,5), (3,6), (4,7)\}$

Question 2

Given the equation $y^2 = x + 3$, is this equation a function of $x$?

Accepted Answer

No, because some $x$ values correspond to more than one $y$ value.

Question 3

What is the domain of the function $f(x) = \sqrt{x-2}$?

Accepted Answer

$[2, \infty)$

Question 4

Which of the following graphs represents a function?

Accepted Answer

A graph where every $x$ value corresponds to exactly one $y$ value.

Question 5

Find the range of the function $f(x) = x^2 + 1$.

Accepted Answer

$[1, \infty)$

Question 6

Given $f(x) = x^2$ and $g(x) = x + 1$, what is $(f + g)(x)$?

Accepted Answer

$x^2 + x + 1$

Question 7

What is the domain of $f(x) = \frac{1}{x-3}$?

Accepted Answer

$(-\infty, 3) \cup (3, \infty)$

Question 8

If $f(x) = x^2$ and $g(x) = 2x$, what is $f(g(x))$?

Accepted Answer

$4x^2$

Question 9

Which transformation results in the graph of $f(x)$ being reflected over the $y$-axis?

Accepted Answer

$f(-x)$

Question 10

What is the equation of a circle with center $(2, -3)$ and radius $5$?

Accepted Answer

$(x-2)^2 + (y+3)^2 = 25$

Question 11

Given $f(x) = x^2$ and $g(x) = x + 1$, what is $f(x-2)$?

Accepted Answer

$(x-2)^2$

Question 12

Which of the following describes a vertical shift of $f(x)$ up by 3 units?

Accepted Answer

$f(x) + 3$

Question 13

If $f(x) = \sqrt{x+4}$, what is the domain of $f(x)$?

Accepted Answer

$[-4, \infty)$

Question 14

Which of the following is the result of reflecting $f(x) = x^3$ over the $x$-axis?

Accepted Answer

$-x^3$

Question 15

Given $f(x) = x^2$ and $g(x) = x + 2$, what is $f(g(x))$?

Accepted Answer

$(x+2)^2$

Question 16

Which of the following is the correct interval notation for all real numbers except $x = 2$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 17

If $f(x) = x^2$ and $g(x) = 3x$, what is $(f \cdot g)(x)$?

Accepted Answer

$3x^3$

Question 18

Which of the following is the standard form of the equation of a circle with center $(1, -2)$ and radius $4$?

Accepted Answer

$(x-1)^2 + (y+2)^2 = 16$

Question 19

Given $f(x) = x^2$ and $g(x) = x + 1$, what is $f(x) - g(x)$?

Accepted Answer

$x^2 - x - 1$

College Algebra: Functions and Graphs (Study Guide)

Study Guide - Practice Questions